The present invention relates to servo systems in data storage devices. In particular, the present invention relates to the linearization of position error signals.
In data storage devices with movable heads, the heads are often positioned based on servo information stored on the storage medium. This servo information is converted into a position signal that indicates the relative position of the head on the disc. Ideally, the position signal is a linear function of the head""s position on the medium.
However, it is well known that MR and GMR heads have non-linearity problems and as head sizes have decreased, it has become more and more difficult to generate a linear position signal. Because of this, a number of compensation techniques have been developed in the art to linearize the position signal.
One group of techniques combines different position signals to form a normalized position signal. In particular, such systems rely on a normal position signal and a quadrature position signal that are 90 degrees out of phase with each other. By arithmetically combining the normal and quadrature position signals, the compensation techniques generate a normalized position signal that is more linear than either the normal position signal or the quadrature position signal. Unfortunately, as heads have gotten smaller, such normalization techniques have been unable to provide a fully linear normalized position signal.
Additional linearization techniques include identifying a polynomial that describes the relationship between the non-linear position signal and the head""s position. This polynomial description is then used to identify the actual position of the head from the position signal.
One problem with fitting a polynomial to a position signal is that the coefficients of the polynomial must be determined within the disc drive itself and the disc drive has limited computing and memory resources for identifying these coefficients. In addition, since the polynomial is determined within the disc drive, the actual position of the head is unknown during the fitting process. This makes it difficult to identify the relationship between the position signal and the actual position of the head.
A method and storage device are provided for initializing a polynomial linearizer in the storage device. The linearizer is initialized by identifying the coefficients of the linearizer polynomial. To reduce the computational intensity of this process, orthogonal-type coefficients for at least two orthogonal polynomials are identified, where the linearizer polynomial is formed as the sum of the orthogonal polynomials. The orthogonal-type coefficients are then combined to identify linearizer coefficients for the linearizer polynomial.